Typically, gas turbine engines operate at high temperatures that may exceed 2,500 degrees Fahrenheit. During operation, turbine engines expose turbine vanes, turbine vane shrouds, and other components to these high temperatures. As a result, turbine vanes and shrouds must be made of materials capable of withstanding such high temperatures. Turbine vanes often contain cooling systems for prolonging the life of the vanes and reducing the likelihood of failure as a result of excessive temperatures. However, these cooling systems often do not include cooling channels for reducing the temperature of seals positioned in seal grooves between adjacent turbine vanes in turbine shrouds. Without adequate cooling, these seals are susceptible to premature failure. Thus, a need exists for a cooling system for seals in seal grooves of turbine vane shrouds to reduce the likelihood of premature failure.